There should be a very simple command that allows you to create a command block with commands already inside it.
Examples:
/give @p minecraft:command_block{Input:[give @p command_block], output:[R:1,C:1,T:1]}
This command will give you a impulse command block, that's conditional and needs redstone to activate it, here's the explanation:
1. The input already has the give @p command_block.
2. R:1 means needs redstone, R:0 means always active.
3. C:1 is conditional and C:0 is unconditional.
4. T:1 is impulse, T:2 is chain and T:3 is repeat command block types.
I believe you can already do that:
/give @p command_block{Command:"say h",auto:1b}
The only thing you can't do, is make it conditional.
You're right, it's already possible. But the tag actually looks like this:
/give @p command_block{BlockEntityTag:{Command:"say this already exists"}}